System and method for Hilbert phase imaging

ABSTRACT

Hilbert phase microscopy (HPM) as an optical technique for measuring high transverse resolution quantitative phase images associated with optically transparent objects. Due to its single-shot nature, HPM is suitable for investigating rapid phenomena that take place in transparent structures such as biological cells. A preferred embodiment is used for measuring biological systems including measurements on red blood cells, while its ability to quantify dynamic processes on the millisecond scale, for example, can be illustrated with measurements on evaporating micron-size water droplets.

BACKGROUND OF THE INVENTION

Optical microscopy has been a commonly used method of investigation inmedicine and biology. Numerous biological samples, including live cells,are quite transparent under visible light illumination and behaveessentially as phase objects. Techniques such as phase contrast andNomarski microscopy provide contrast of nearly invisible samples bytransforming the phase information into intensity distribution and thusreveal structural details of biological systems. However, theinformation obtained with these techniques about the phase shiftassociated with the illuminating field is only qualitative. Retrievingquantitative phase information from transparent objects with highaccuracy and low noise allows for measurements in the biologicalinvestigation of structure and dynamics. Both interferometric andnon-interferometric techniques have been proposed for quantitative phaseimaging of biological samples. Also Fourier phase microscopy (FPM) hasbeen developed as an extremely low-noise phase imaging method. Due tothe sub-nanometer phase stability over extended periods of time, FPM issuitable for investigating dynamics in biological systems on time scalesfrom seconds to a cell lifetime.

SUMMARY OF THE INVENTION

Many processes that take place at the cellular level, includingcytoskeletal dynamics, cell membrane fluctuations and neural activityoccur at shorter time scales, down to the millisecond range. Therefore,a microscope that allows acquisition of full-field quantitative phaseimages at kHz frame rates enables quantification of biological systems.

The complex analytic signal formalism of time-varying fields has foundbroad applications in optics. In particular, the Hilbert transformrelationship between the real and imaginary part of a complex analyticsignal has been used to retrieve phase shifts from single temporalinterferograms. The present invention relates to systems and methods forquantitative phase imaging, referred to as Hilbert phase microscopy(HPM), which allows the retrieval of a full field phase image from asingle spatial interferogram.

In HPM, single-shot phase imaging is limited in frame acquisition rateonly by the recording device such as an imaging sensor. Examples ofimaging sensors include digital imaging detectors such as charge coupleddevices (CCD) or a CMOS imaging array. This contrasts withphase-shifting techniques, in which multiple recordings are required forretrieving a single phase image. In addition, HPM provides for phaseunwrapping, which enables the study of phase objects much larger thanthe wavelength of light. The imaging device preferably has at least200,000 pixels that can collect at least 10 frames per second andpreferably over 100 frames per second.

A preferred embodiment splits the light from a single light source alonga reference path and a sample path. The light along the sample path isdirected through the sample or object being measured and the light alongthe reference path is modulated by a modulating element such that whenthe light from the sample is combined with the modulated reference lightthat an interference pattern is produced that is detected by the imagingsensor. The modulating element can be a rotating mirror or a movablelens, for example. Preferred embodiments of the invention can includefiber optics to couple light onto the object such as tissue to beimaged. Lasers or other highly coherent light sources of differentwavelengths can be used. A computer or other data processor or imageprocessor can be connected to the output of the imaging device forprocessing of the image data. In a preferred embodiment, the dataprocessor is programmed with a software program to process the image byfirst removing noise using a selected point in the field of view as areference. The image then undergoes a Hilbert transform to obtain aprocessed image. A Fourier transform is performed on the interferogramfollowed by application of a filter to obtain filtered image data. Thisis followed by application of an inverse Fourier transform to obtainwrapped and unwrapped phase images. This provides quantitative phaseimages of the object of interest.

Preferred embodiments of the invention can include configurations ofHilbert phase imaging according to the invention in which the opticalgeometry is set up for transmissive or reflective imaging. In apreferred embodiment an inverted microscope geometry can be used with abeam splitter used to combine the reference and sample images. Areflective measurement can be performed by attaching a reflectivematerial, such as polystyrene beads to a cell membrane. Coherent lightcan then be reflected off this material to obtain an interferogram. Thiscan be used to measure mechanical properties of the membrane such as theshear modulus or the bending modulus. The procedures described hereincan used in-vitro on human or mammalian tissue or fluid or in-vivo onthe human eye of other tissues, for example.

The invention provides for non-biological applications as well asbiological applications; for instance the invention can provide forstudying the phase profile of an optical fiber and/or other transparentor semi-transparent objects or materials including crystallinestructures.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a preferred embodiment of an imaging system inaccordance with the invention.

FIGS. 2 a-2 h illustrate images obtained including a) transmissionintensity image; b) interferogram, c) sinusoidal signal, and d) wrappedphase measured from the rectangular area indicated in a); e) full-fieldunwrapped phase; f) full-field quantitative phase image; g) transverseprofile through the phase image in f with the continuous line indicatingthe modeled fit; h) HPM image of a whole blood smear (magnification 40);the 5 μm scale bar is indicated; the gray scale bars indicate intensitylevels for a-c, and phase in radians for d-h.

FIGS. 3 a-3 d are images obtained including a) HPM image of waterdroplets; the color bar indicates thickness in microns and the scale baris 10 μm; b) path-length fluctuations of point O of FIG. 3 a; thestandard deviation is indicated; c) droplet mass (femto-gram units)temporal evolution during evaporation; d) maximum thickness of dropletsduring evaporation; with data being collected over a 3.4 s timeinterval, and with 10.3 ms between successive frames.

FIG. 4. illustrates a preferred embodiment of an imaging system inaccordance with the invention.

FIGS. 5 a-5 c illustrate images and data obtained including a)Quantitative phase image of whole blood smear; the volumes of RBCs (redblood cells) are indicated in femtoliters and the colorbar is inradians, and b) Temporal fluctuations of the spatial standard deviationassociated with area O, and c) temporal average sigma.sub.s as functionof averaging frames.

FIGS. 6 a-6 d illustrates quantitative assessment of the shapetransformation associated with a red blood cell during a 10 secondperiod.

FIGS. 7 a-7 i illustrate images and data obtained including a-e) variousstages of hemolysis during a 4 second period, and f-h) phase images ofhemoglobin expelled from the cell corresponding to t=0.5 s, 1.0 s and1.5 s, as indicated, and i) cell volume change and optical path-lengthshift associated with a point outside the cell (indicated by the arrowin FIG. 7 f) during the 4 s period.

FIG. 8 is a process sequence used in a software program to process imagedata in accordance with a preferred embodiment of the invention.

DETAILED DESCRIPTION OF THE INVENTION

A preferred embodiment of the invention is illustrated in FIG. 1. Inthis embodiment a HeNe laser is used as a light source 10 for an imagingMach-Zender interferometer 20. A first beam splitter 12 splits the beamfrom the light source 10 to form two arms of the interferometer, thearms comprising a reference beam 14 and a sample beam 16, respectively.A mirror 18 directs the sample beam 16 onto a sample or object 25. Ineach arm of the interferometer 20 there are two telescopic systems, withmagnification M=20 for example, each telescopic system comprises anobjective 22, 24 and a lens 26, 28. A second mirror 30 directs thereference field onto a second beam splitter 32. The orientation of thereference field 40 is adjustable, for example, by rotatable movement ofmirror 30 in order to tilt reference field 40. An image sensor 42, suchas a CCD, can be positioned in the common Fourier plane of the lenses26, 28 where the exact (magnified) replica of the sample field 44 isformed. The reference field 40, which is directed onto the CCD imagesensor 42 by the beam splitter 32, is slightly tilted with respect tothe sample beam 44 in order to create a uniform fringe structureoriented at 45° with respect to the x and y axes of the CCD image sensor42. The CCD used in this embodiment (C770, Hamamatsu Photonics) has anacquisition rate of 291 frames/s at the full resolution of 480×640pixels. Higher resolutions and acquisition rates can also be used. Imagedata is sent from the sensor 42 to the processor or computer 120 foranalysis and display.

For a given sample 25, the spatially varying irradiance at the imageplane across either the x or y axis has the form:I(x)=I _(R) +I _(S)(x)+2√{square root over (I _(R) )} I _(S)(x)cos[qx+φ(x)]  (1)

where I_(R) and I_(S) are, respectively, the reference and sampleirradiance distributions, q is the spatial frequency of the fringes, andφ is the spatially varying phase associated with the object 25, thequantity of interest. Eq. (1) is analogous to describing the temporalinterference in Michelson and other interferometers, in which qcorresponds to the frequency shift introduced by an acousto-opticmodulator or a moving mirror. For the transparent objects of interesthere, I_(s)(x) is expected to have a weak dependence on x. By adjustingthe magnification of the system, the spatial frequency q can be chosento match or exceed the maximum frequency allowed by the numericalaperture of the instrument, such that the diffraction-limited resolutionis preserved. The sinusoidal term u(x)=2√{square root over (I_(R)I_(S))} cos[qx+φ(x)] can be isolated by Fourier high-pass filtering. Itfollows that the complex analytic signal, z(x), associated with the realfunction u(x) can be obtained as $\begin{matrix}{{z(x)} = {{\frac{1}{2}{u(x)}} + {i\frac{P}{2\pi}{\int_{- \infty}^{\infty}{\frac{u\left( x^{\prime} \right)}{x - x^{\prime}}{\mathbb{d}x^{\prime}}}}}}} & (2)\end{matrix}$In Eq. 2, the imaginary part of the right hand side stands for aprinciple value (P) integral, identifiable as the Hilbert transform ofu(x). Therefore, the phase spectrum, φ(x), associated with the complexanalytic signal, z(x), is calculated asφ(x)=tan⁻¹ {Im[z(x)]/Re[z(x)]}  (3)Note that z(x) exhibits rapid phase modulation, with frequency q, andthus φ is strongly wrapped. However, since q is higher than the spatialfrequency content of the object, the unwrapping procedure worksefficiently. Finally, the phase associated with the object, φ(x), isextracted simply asφ(x)=φ(x)−qx.  (4)

This procedure can be used to retrieve the phase profile of an opticalfiber, for example. In a preferred embodiment, the invention providesfor an apparatus and method for retrieving the phase profile of anoptical fiber having a fiber core with a diameter of 100 μm and arefractive index of 1.457, while the cladding has an outer diameter of110 μm and a refractive index of 1.452. The fiber is immersed inglycerol to better mimic a phase object, in this example. Thetransmission intensity image of this sample (FIG. 2 a) shows lowcontrast, which is an indication of the transparency of the sample.FIGS. 2 b-d represent intermediate steps in the phase reconstructionsequence and correspond to the rectangular area shown in FIG. 2 a. Thisregion encompasses the glycerol/cladding and cladding/core interfaces.The interferogram recorded by the CCD (FIG. 2 b) is Fourier transformedand high-pass filtered, such that the sinusoidal signal is obtained(FIG. 2 c). In order to obtain the complex analytic signal associatedwith this real signal, the 2D Fourier transform is computed and thenegative spatial frequencies are suppressed. Upon the inverse Fouriertransform operation a complex 2D signal is obtained that uniquelyprovides information about the phase of the object, as described in Eq.2. The strongly wrapped and unwrapped phase images, respectively, areshown in FIGS. 2 d and 2 e. The quantitative phase image of the opticalfiber is obtained by subtracting the linear phase and is depicted inFIG. 2 f, while a cross-section is shown in FIG. 2 g. The continuousline represents the modeled fit, with the refractive index of glycerolas the variable parameter. The refractive index of glycerol for the bestfit has a value of n=1.467, which approximates known values.

A preferred embodiment of the invention uses HPM for biologicalmeasurements, such as, for example, quantifying parameters forphase-images of tissue or body fluids such as red blood cells from wholeblood smears. FIG. 2 h shows an example of such an image, in which theindividual cells and agglomeration of cells are easily identifiable. Redblood cells lack nuclei and major organelles can be modeled as opticallyhomogeneous objects. Thus, the phase information from the HPM images canbe transformed into thickness information, which directly providesparameters such as cell shape and volume. In this example, the data wererecorded in 10.3 ms and the sample was prepared by sandwiching a dropletof whole blood between two cover slips.

Thus, according to preferred embodiments of the invention, HPM canprovide quantitative phase images in transparent samples. In addition,this method can measure phase objects with phase profiles much higherthan the wavelength of the illuminating light. This important feature isdue to the high spatial modulation imposed on the image, which createswell defined wrapping points on the phase image, thus facilitating theunwrapping procedure. The ability of HPM to obtain quantitative phaseimages from single-shot measurements allows, therefore, monitoring fastdynamic processes in transparent or transmissive systems.

A further preferred embodiment of the invention provides for studyingrapid processes in transparent media, such as, for example, analyzingthe evaporation of micron-size liquid droplets. FIG. 3 a shows the FPMimage of such water droplets sprayed onto a microscope slide. The z-axisinformation indicates that the thickness of these droplets issignificantly smaller than their transverse size. In order to monitorthis evaporation phenomenon, a series of 333 phase images were recordedat time intervals of 10.3 ms. Since each phase image is obtained fromone CCD recording, it is not necessary to eliminate noise between thetwo interferometer arms, which provides a significant advantage overphase-shifting techniques. The noise between successive frames does notobscure the phase images, which can be conveniently displayed byreferencing each image to a fixed point in the field of view. Thisreference point is denoted in FIG. 2 a by “R”. In order to quantify theresidual transverse noise present in the phase image series, temporalpath-length fluctuations associated with point 0 indicated in FIG. 3 awere recorded. These fluctuations were averaged over an areacorresponding to the diffraction-limited spot of the imaging optics(0.45×0.45 μm²). The standard deviation of these fluctuations has avalue of 1.32 nm, as shown, which indicates that nanometer path-lengthsensitivity can be obtained on the millisecond time scale. FIG. 3 cshows the evolution of droplet masses during this recording, ascalculated from the HPM images. For diffraction-limited transverseresolution and the current phase sensitivity, HPM is sensitive to waterevaporation volumes that are remarkably small, on the order of 10⁻¹⁸liters. In addition, the quantitative phase images offer detailed 3Dinformation about these homogeneous structures. Thus, the temporaldependencies of the maximum thickness associated with the evaporatingdroplets can be easily estimated (FIG. 3 d). These curves aresignificantly more irregular (sometimes non-monotonous) than the timeevolution of the mass, which indicates the discontinuous nature ofchanges in shape during evaporation.

Preferred embodiments of the invention provide advantages. For instance,Hilbert phase microscopy according to the invention can retrieve hightransverse resolution quantitative phase images from single-shotmeasurements with nanometer-level sensitivity. Applying complex analyticsignals to the spatial domain is based on the analogy that existsbetween the equations describing the temporal and spatial fluctuationsof electromagnetic fields. HPM provides a method for measuring rapidphenomena in transparent media, including the dynamics of biologicalsystems and living cells.

Turning now to FIG. 4, a further preferred embodiment of the inventionuses the principle of Hilbert phase microscopy in an inverted geometryto provide a high-speed and high-sensitivity quantitative phasemicroscope 60. The inverted geometry is particularly suitable for livecell investigation. The potential of the method for quantitativebiological microscopy has been demonstrated by quantifying red bloodcell shape and fluctuations with nanometer path-length sensitivity atthe millisecond time scale.

Referring to FIG. 4, a preferred embodiment extends HPM by integratingit with an inverted microscope 60. A light source 50, such as, forexample, a HeNe laser (λ=632 nm) is coupled by first mirror 52 andsecond mirror 54 into a 1×2 single-mode, fiber-optic coupler 56 andsplit through fiber splitter 58 to a reference arm 64, comprising afirst fiber coupler output 66 and collimator 68, and to a sample arm 62,comprising a second fiber coupler output 72 and collimator 74. The firstoutput field provided through the sample arm acts as the illuminationfield for an inverted microscope 80 equipped with a 100X objective 88.The tube lens 90 is such that the image of the sample 85 is formed atthe plane of the image sensor CCD 100 via the beam splitter cube 92. Thesecond fiber coupler output 66 is collimated by collimator 68 andexpanded by a telescopic system consisting of second microscopeobjective 70 and the tube lens 90. This reference field beam can beapproximated by a plane wave, which interferes with the sample imagefield 96. The reference field 94 is tilted with respect to the samplefield 96 (for example, by adjusting collimator 68), such that uniformfringes are created at an angle of 45° with respect to x and y axes ofthe CCD 100. The CCD used (C7770, Hamamatsu Photonics) has anacquisition rate of 291 frames/s at the full resolution of 640×480pixels and the CCD 100 can be connected to and controlled by computer120. In this example, the focal distance, ƒ, between the focus of thereference arm objective 3 and the tube lens 90 is 250 mm.

The spatial irradiance associated with the interferogram across onedirection is given by Eq. 1, above, where I_(R) and I_(s)(x) are,respectively, the reference and sample irradiance distributions, q isthe spatial frequency of the fringes, and φ(x) is the spatially varyingphase associated with the object 85, φ(x) being an important quantity ofinterest in the analysis. Using high-pass spatial filtering to isolatethe sinusoidal term u(x)=2√{square root over (I_(R)I_(S))}cos[qx+φ(x)],as described above, and applying the Hilbert transformation as in Eq. 2above to obtain the complex analytical signal, z(x), (and thereby thephase spectrum φ(x) through Eq. 3), again, by Eq. 4, the quantity φ(x)can be retrieved for each point of the single-exposure image.

Owing to the inverted geometry, the new HPM microscope is particularlysuited for the quantitative investigation of live cells. To demonstratethe ability of the new instrument to quantify cellular structures at themillisecond and nanometer scales, time-resolved HPM images of red bloodcells (RBCs) were obtained. Droplets of whole blood were sandwichedbetween cover slips, with no additional preparation. FIG. 5 shows aquantitative phase image of live blood cells; both isolated andagglomerated erythrocytes are easily identifiable. A white blood cell(WBC) is also present in the field of view. Using the refractive indexof the cell and surrounding plasma of 1.40 and 1.34, respectively, thephase information associated with the RBCs can be easily translated intoa nanometer scale image of the cell topography. In addition, the volumeof individual cells can be evaluated; in FIG. 5, the measured volumes(units of in femtoliters) are displayed below individual red bloodcells.

In order to eliminate the longitudinal noise between successive frames,each phase image was referenced to the average value across the area inthe field of view containing no cells, denoted by R. To quantify thestability of the instrument and thus the sensitivity to dynamicalchanges of cell topography, sets of 1000 images were recorded, acquiredat 10.3 ms each and noise analysis was performed on a second emptyregion in the field of view. The spatial standard deviation, σ_(s), ofthe pathlength fluctuation across this area (indicated in FIG. 5 a as O)has a certain fluctuation in time and is characterized in turn by atemporal average <σ_(s)>. The time-dependence of σ_(s) is plotted inFIG. 5 b, while the mean value <σ_(s)> versus the number of averagingframes is shown in FIG. 5 c. Remarkably, <σ_(s)> is lowered to less than1 nm values by averaging only 2 successive frames. This noise assessmentdemonstrates that the inverted HPM instrument according to a preferredembodiment of the invention is capable of providing quantitativeinformation about structure and dynamics of biological systems, such asRBCs, at the sub-nanometer scale.

An example of significant dynamical change of a live red blood cell isshown in FIGS. 6 a and 6 c. The phase images correspond to the red bloodcell shown in FIG. 5 a and are acquired 10.3 ms apart and represent thefirst and the last frames in a 1,000 frame data set. FIGS. 6 b and 6 dshow the horizontal and vertical thickness profiles of the cell at thetwo stages, with nanometer accuracy. Interestingly, the significantchange in the cell shape is due to a rapid interaction with theneighboring white blood cell, at the lower left comer of the image (alsoshown as WBC in FIG. 5 a). This results in a rapid asymmetric shapechange that is easily quantified by HPM. This remarkable result cannotbe quantified by techniques such as atomic force or electron microscopy.

Hemolysis (RBC “lysing”) is a phenomenon in which the erythrocytemembrane ruptures and the cell loses its hemoglobin content. Thisprocess has been studied recently in the context of optical clearing.Using the HPM instrument, a sequence of 1,000 phase images was used, at10.3 milliseconds acquisition time, to dynamically quantify the changesin the cell as the result of spontaneous lysing. FIGS. 7 a-7 e depictthe cell volume decrease during various stages of hemolysis. Note theunusual flat shape of the cell. The phase shifts owing to the expelledhemoglobin can be observed in FIGS. 7 f-7 h, where only the regionsurrounding the cell is represented, to avoid gray-scale saturation. Themembrane rupture is highly localized, as indicated by the asymmetry inthe FIGS. 7 f-7 h, and the hemoglobin appears to be diffusing from apoint source on the cell. The RBC volume was evaluated during theprocess and its temporal dependence is plotted in FIG. 7 i. During thishighly dynamic process, the volume of the cell decreases by 50% in lessthan 4 seconds (the signal was averaged over 2 frames). On the otherhand, the phase shift associated with a point in close proximity to thecell reaches a steady-state maximum level of almost 9 nm in about onesecond. In order to improve the signal to noise of this ultra-sensitivemeasurement, the signal was averaged in space over 11×11 pixels and intime over 10 frames. The resulting standard deviation of these datareached the remarkably low value of 0.09 nm. The measured phase shift islinearly proportional to the local concentration of hemoglobin; thus,the roughly constant path-length shift reached after about 1500 ms canbe interpreted as the result of equilibrium between the generation ofmolecules from the cell and the diffusion process.

A preferred method of performing Hilbert phase microscopy is shown inthe process sequence 200 of FIG. 8. This process can be performed usinga software program on a computer. First, a calibration step 202 canoptionally be performed by obtaining an image of a known sample, whichcan then be used to remove background noise in the system. A sample tobe measured is then mounted in a holder and one or more interferogramimages of the sample are collected 204. A Fourier transform is thenapplied 206 to each image, following by filtering of the image 208. Theinverse Fourier transform is then applied 210 followed by noise removal212. A phase unwrapping step 214 and determination of other quantitativeproperties of the sample can then be obtained 216.

Preferred embodiments of the invention can include configurations ofHilbert phase imaging according to the invention in which the opticalgeometry is set up for transmissive and/or reflective mode.

The invention provides for non-biological applications as well asbiological applications; for instance the invention can provide forstudying the phase profile of an optical fiber and/or other transparentor semi-transparent objects or materials. Preferred embodiments of theinvention may employ a laser or other coherent light source as part ofthe light source optics. Wavelength from the ultraviolet visible orinfrared region of the electromagnetic spectrum can be used.

Advantages of the invention include the speed and simplicity ofobtaining quantitative image data. The inverted Hilbert phase microscopeis capable of measuring quantitative phase images of cells at thesub-nanometer and millisecond scales. The inverted geometry makes thenew instrument particularly appealing for quantitative cell biology,such as, for example, without limitation, the non-contactcharacterization of erythrocyte membrane mechanics.

Biological structures such as living cells are predominantly transparentunder bright field illumination. Phase contrast (PC) and differentialinterference contrast (DIC) microscopy have been used extensively toinfer morphometric features of cells without the need for exogenouscontrast agents. These techniques transfer the information encoded inthe phase of the imaging field into the intensity distribution of thefinal image. Thus, the optical phase shift through a given sample can beregarded as a powerful endogenous contrast agent, as it containsinformation about both the thickness and refractive index of the sample.From this point of view, mature erythrocytes (red blood cells, or RBCs)represent a very particular type of structure in that they lack nucleiand major organelles. Thus, RBCs can be modeled as optically homogeneousobjects, i.e., they produce local, optical, phase shifts that areproportional to their thickness. Therefore, measuring quantitative phaseimages of red blood cells provides cell thickness profiles with anaccuracy that corresponds to a very small fraction of the opticalwavelength. Such nanoscale topographic information provides insight intothe biophysical properties and health state of the cell. Cells withnuclei or optically opaque components can be measured using thereflective process described earlier.

Further preferred embodiments according to the invention provide methodsfor quantifying rapid biological phenomena, such as millisecond scaleRBC membrane fluctuations, using Hilbert phase microscopy (HPM) as atechnique complementary to Fourier phase microscopy (FPM). HPM extendsthe concept of complex analytic signals to the spatial domain andmeasures quantitative phase images from only one spatial interferogramrecording. Due to its single-shot nature, the HPM acquisition time islimited only by the recording device and thus can be used to accuratelyquantify nanometer level path-lengths shifts at the millisecond timescales or less, where many relevant biological phenomena develop. Imagesare preferably obtained in less than a one second time period and inmost applications in less than 100 milliseconds. As a result, videorecording of dynamic events can be recorded at the cellular level.

While the invention has been described in connection with specificmethods and apparatus, it is to be understood that the description is byway of example of equivalent devices and methods and not as a limitationto the scope of the invention as set forth in the claims.

1. A method of imaging an object comprising: providing a light source, afirst optical path including an object to be imaged, a second opticalpath and an imaging device; positioning the imaging device relative tothe first optical path and the second optical path; orienting the firstoptical path relative to the second optical path to form a fringestructure; obtaining an image of the fringe structure; and processingthe image with a Hilbert transform to obtain image data.
 2. The methodof claim 1 further comprising orienting the fringe structure at an angleof 45° with respect to orthogonal axes of the imaging device.
 3. Themethod of claim 1 further comprising imaging a biological material. 4.The method of claim 1 further comprising imaging tissue.
 5. The methodof claim 1 further comprising providing a laser light source and acharge coupled device in a Fourier plane of the first optical path andthe second optical path that detects an image.
 6. The method of claim 1further comprising obtaining a quantitative spatial phase image of theobject.
 7. The method of claim 6 further comprising obtaining thespatial phase image of the object by: Fourier-transforming and high-passfiltering the measured spectral data to obtain a real sinusoidal signalcomponent of a complex analytic signal; obtaining the complex analyticsignal associated with the sinusoidal signal by computing a 2D Fouriertransform and suppressing the negative frequencies by employing anHilbert transformation; taking an inverse Fourier transform to obtain acomplex 2D signal that provides phase information about the object; andobtaining the quantitative spatial phase image by subtracting the linearphase.
 8. The method of claim 1 further comprising removing a tissue orblood ample from a mammalian body for measurement.
 9. The method ofclaim 1 further comprising determining a size of a sample from an imageof the sample.
 10. The method of claim 1 further comprising determininga volume of an object in a sample.
 11. The method of claim 1 furthercomprising imaging a blood cell.
 12. The method of claim 1 furthercomprising measuring a characteristic of a red or white blood cell. 13.The method of claim 1 further comprising measuring a noise component inan image and removing the noise component from the image.
 14. The methodof claim 1 further comprising obtaining an image with light reflected byan object.
 15. The method of claim 14 further comprising attaching areflective material to an object being measured.
 16. The method of claim15 further comprising attaching polystyrene particles to the object. 17.The method of claim 1 further comprising measuring hemolysis of a redblood cell.
 18. The method of claim 1 further comprising using anoptical modulator to modulate light from the light source.
 19. Themethod of claim 1 further comprising measuring a crystalline material.20. The method of claim 1 further comprising measuring an optical fiber.21. A Hilbert phase imaging device comprising: a light source, a firstoptical path, a second optical path and an imaging device positioned toreceive light directed along the first optical path and the secondoptical path; a modulating element that positions light from the lightsource to form a detectable fringe structure at the imaging device; anda processor that receives image data from the imaging device andperforms a Hilbert phase transformation of the image.
 22. The device ofclaim 21 further comprising a fiber optic device that couples light fromthe light source to the first optical path and the second optical path.23. The device of claim 21 wherein a beam splitter combines a modulatedreference image and a sample image.
 24. The device of claim 21 whereinthe modulating device comprises a movable mirror.
 25. The device ofclaim 21 wherein the modulating element comprises tilting the firstlight path relative to the second light path.
 26. The device of claim 21wherein a sample is mounted relative to an inverted microscope.
 27. Thedevice of claim 26 wherein the inverted microscope includes a sampleholder, an objective lens, a beam splitter and a lens that couples lightonto the imaging device positioned in a common Fourier plane.
 28. Thedevice of claim 22 further comprising a fiber optic splitter, a fibercoupler, a first collimator, a second collimator and a second objectivelens.
 29. The device of claim 21 wherein the processor includes aprogram that performs a Fourier transform on image data, applies afilter to the transformed image data and performs an inverse Fouriertransform on the filtered image data.
 30. The device of claim 21 furthercomprising a blood or tissue sample holder.
 31. The device of claim 21wherein light is reflected by a sample.
 32. The device of claim 21wherein light is transmitted through the sample.
 33. The device of claim21 wherein a reflective material is positioned on the sample.
 34. Thedevice of claim 21 wherein the imaging device comprises a CCD or CMOSimaging device leaving at least 480×640 pixels and operating at least 10frames per second.
 35. An imaging device comprising: a light source, afirst optical path, a second optical path and an imaging devicepositioned relative to the first optical path and the second opticalpath; the first optical path comprises an objective lens; a samplepositioned relative to the first optical path to provide an interferencepattern; a processor that provides Fourier transform and filteroperations on image data to provide phase image data of the sample. 36.The device of claim 35 further comprising a rotating mirror.
 37. Thedevice of claim 35 wherein the imaging device collects at least 10frames per second.
 38. The device of claim 35 wherein the processorperforms a Hilbert transform on the image data.
 39. The device of claim35 comprising an interferometer.
 40. The device of claim 35 comprising amicroscope.